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Media type:
E-Article
Title:
An Analytic Version of Wiener-Itô Decomposition on Abstract Wiener Spaces
Contributor:
Lee, Yuh-Jia;
Shih, Hsin-Hung
Published:
Mathematical Society of the Republic of China, 2019
Published in:
Taiwanese Journal of Mathematics, 23 (2019) 2, Seite 453-471
Language:
English
ISSN:
1027-5487;
2224-6851
Origination:
Footnote:
Description:
In this paper, we first establish an analogue of Wiener-Itô theorem on finite-dimensional Gaussian spaces through the inverse S-transform, that is, the Gauss transform on Segal-Bargmann spaces. Based on this point of view, on infinite-dimensional abstract Wiener space (H, B), we apply the analyticity of the S-transform, which is an isometry from the L²-space onto the Bargmann-Segal-Dwyer space, to study the regularity. Then, by defining the Gauss transform on Bargmann-Segal-Dwyer space and showing the relationship with the S-transform, an analytic version of Wiener-Itô decomposition will be obtained.